Synchronization transition is monotonous (in fact, there exists
a Lyapunov function that governs it), but it can be generally hardly
expressed analytically.
An analytic solution is, however, possible,
if the Ott-Antonsen (OA) ansatz [1]}, which
applies to the thermodynamic limit \(N\rightarrow \infty \) , is peformed.
In the OA ansatz it is assumed that
the distribution of the phases is a wrapped Cauchy
distribution, and the complex circular moments
\(Z_k=\langle e^{i k\varphi }\rangle \) 
